The hypothesis for this AIDS Clinical Trial Group (ACTG) study is that human immunodeficiency virus globulin (human) IV (HIVIG) will decrease the viral burden of moderately advanced HIV-positive children. HIVIG is a preparation of highly purified human immune globulin containing high titers of antibody to HIV structural proteins. The primary objectives of this trial are 1) to evaluate the safety and tolerance of HIVIG in HIV-infected children 2) to evaluate the dosage and pharmacokinetics of HIVIG by serial measurements of immunoglobulins, anti-p24 antibody and rubella antibody titers and 3) to evaluate the antiviral activity of HIVIG at 3 dosage levels by assays of viral burden, and neutralizing antibody titers.